Skip to main content
SpringerLink
Log in

Cluster consensus for second-order mobile multi-agent systems via distributed adaptive pinning control under directed topology

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper investigates adaptive pinning control for cluster consensus of second-order mobile multi-agent systems with inherent nonlinear dynamics under fixed directed topologies. Using tools from matrix, graph and Lyapunov stability theories, sufficient conditions for cluster consensus are obtained by virtue of a distributed adaptive pinning control scheme. Moreover, an adaptive strategy on the strengths is designed to guarantee that the cluster consensus condition does not require any global information except a connection assumption. The obtained results are also extended to complete consensus for second-order mobile multi-agent systems. Finally, numerical simulations are presented to illustrate the theoretical results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Vicsek, T., Czirk, A., Ben-Jacob, E., Cohen, O., Shochet, I.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)

    Article  Google Scholar 

  2. Olfati-Saber, R., Fax, J., Murray, R.: Consensus and cooperation in networked multi-agent systems. Proc. IEEE 95, 215–233 (2007)

    Article  Google Scholar 

  3. Cao, Y.C., Yu, W.W., Ren, W., Chen, G.R.: An overview of recent progress in the study of distributed multi-agent coordination. IEEE Trans. Ind. Inf. 9, 427–438 (2013)

    Article  Google Scholar 

  4. Balch, T., Arkin, R.: Behavior-based formation control for multirobot teams. IEEE Trans. Robot. Autom. 14, 926–939 (1998)

    Article  Google Scholar 

  5. Wang, X., Chen, G.: Synchronization in scale-free dynamical networks: robustness and fragility. IEEE Trans. Circuits Syst. I Regul. Pap. 49, 54–62 (2002)

    Article  Google Scholar 

  6. Mahmoud, M., Mahmoud, E.: Complete synchronization of chaotic complex nonlinear systems with uncertain parameters. Nonlinear Dyn. 62, 875–882 (2010)

    Article  MATH  Google Scholar 

  7. Yu, W., Chen, G., Lv, J.: On pinning synchronizaton of complex dynamical networks. Automatica 45, 429–435 (2009)

    Article  MATH  Google Scholar 

  8. Sun, J., Shen, Y., Zhang, G., Xu, C., Cui, G.: Combination–combination synchronization among four identical or different chaotic systems. Nonlinear Dyn. 73, 1211–1222 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Olfati-Saber, R., Murray, R.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49, 1520–1533 (2004)

    Article  MathSciNet  Google Scholar 

  10. Ren, W., Beard, R.: Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Autom. Control 50, 655–661 (2005)

    Article  MathSciNet  Google Scholar 

  11. Xie, G., Wang, L.: Consensus control for a class of networks of dynamic agents. Int. J. Robust Nonlinear Control 17, 941–959 (2007)

    Article  MATH  Google Scholar 

  12. Tian, Y., Liu, C.: Consensus of multi-agent systems with diverse input and communication delays. IEEE Trans. Autom. Control 53, 2122–2128 (2008)

    Article  MathSciNet  Google Scholar 

  13. Hong, Y., Hu, J., Gao, L.: Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42, 1177–1182 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ren, W., Atkins, E.: Distributed multi-vehicle coordinated control via local information exchange. Int. J. Robust Nonlinear Control 17, 1002–1033 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  15. Yu, W., Ren, W., Zheng, W., Chen, G., Lv, J.: Distributed control gains design for consensus in multi-agent systems with second-order nonlinear dynamics. Automatica 49, 2107–2115 (2013)

    Article  Google Scholar 

  16. Mei, J., Ren, W., Ma, G.: Distributed coordination for second-order multi-agent systems with nonlinear dynamics using only relative position measurements. Automatica (2013). doi:10.1016/j.automatica.01.058

    Google Scholar 

  17. Xu, C., Zheng, Y., Su, H., Zhang, C., Chen, M.: Necessary and sufficient conditions for distributed containment control of multi-agent systems without velocity measurement. IET Control Theory Appl. 8, 1752–1759 (2014)

    Article  MathSciNet  Google Scholar 

  18. Xu, C., Zheng, Y., Su, H., Wang, H.: Containment control for coupled harmonic oscillators with multiple leaders under directed topology. Int. J. Control 88, 248–255 (2015)

    Article  MathSciNet  Google Scholar 

  19. Su, H., Jia, G., Chen, M.: Semi-global containment control of multiagent systems with input saturation. IET Control Theory Appl. 8, 2229–2237 (2014)

    Article  MathSciNet  Google Scholar 

  20. Olfati-Saber, R.: Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Trans. Autom. Control 51, 401–420 (2006)

    Article  MathSciNet  Google Scholar 

  21. Su, H., Wang, X., Lin, Z.: Flocking of multi-agents with a virtual leader. IEEE Trans. Autom. Control 54, 293–307 (2009)

    Article  MathSciNet  Google Scholar 

  22. Li, Z., Ren, W., Liu, X., Xie, L.: Distributed consensus of linear multi-agent systems with adaptive dynamic protocols. Automatica 49, 1986–1995 (2013)

  23. Trentelman, H., Takaba, K., Monshizadeh, N.: Robust synchronization of uncertain linear multi-agent systems. IEEE Trans. Autom. Control 58, 1511–1523 (2013)

    Article  MathSciNet  Google Scholar 

  24. Lu, W., Liu, B., Chen, T.: Cluster synchronization in networks of coupled nonidentical dynamical system. Chaos 20, 013120 (2010)

    Article  MathSciNet  Google Scholar 

  25. Ma, Q., Lu, J.: Cluster synchronization for directed complex dynamical networks via pinning control. Neurocomputing 101, 354–360 (2013)

    Article  Google Scholar 

  26. Su, H., Rong, Z., Chen, M., Wang, X., Chen, G., Wang, H.: Decentralized adaptive pinning control for cluster synchronization of complex dynamical networks. IEEE Trans. Cybern. 43, 394–399 (2013)

    Article  Google Scholar 

  27. Yu, J., Wang, L.: Group consensus in multi-agent systems with switching topologies and communication delays. Syst. Control Lett. 59, 340–348 (2010)

    Article  MATH  Google Scholar 

  28. Han, Y., Lu, W., Chen, T.: Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs. IEEE Trans. Neural Netw. Learn. Syst. 24, 566–578 (2013)

    Article  Google Scholar 

  29. Lu, X., Auatin, F., Chen, S.: Cluster consensus of second-order multi-agent systems via pinning control. Chin. Phys. B 19, 120506 (2010)

    Article  Google Scholar 

  30. Feng, Y., Xu, S., Zhang, B.: Group consensus control for double-integrator dynamic multiagent systems with fixed communication topology. Int. J. Robust Nonlinear Control 24, 532–547 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  31. Chen, J., Chi, M., Guan, Z., Liao, R., Zhang, D.: Multiconsensus of second-order multiagent systems with input delays. Math. Probl. Eng. (2014). doi:10.1155/2014/424537

  32. Chen, Y., Lv, J., Han, F., Yu, X.: On the cluster consensus of discrete-time multi-agent systems. Syst. Control Lett. 60, 517–523 (2011)

    Article  MATH  Google Scholar 

  33. Qin, J., Yu, C.: Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition. Automatica 49, 2898–2905 (2013)

    Article  MathSciNet  Google Scholar 

  34. Horn, R., Johnson, C.: Matrix analysis. Cambridge University Press, Cambridge, UK (1985)

  35. Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

  36. Slotine, J.-J.E., Li, W.: Applied nonlinear control. Prentice-Hall, Englewood Cliffs, NJ (1991)

    MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by National Natural Science Foundation (NNSF) of China under Grant Nos. 61273157, 61374139, 61374053, 61473129, the Program for New Century Excellent Talents in University from Chinese Ministry of Education under Grant NCET-12-0215, the Program for Changjiang Scholars and Innovative Research Team in University under Grant IRT1245, Natural Science Foundation of Ministry of Education in Hunan Province (12C0077, 13C038).

Author information

Authors and Affiliations

  1. School of Sience, Hunan University of Technology, Zhuzhou, 412008, China

    Chengjie Xu

  2. National Key Laboratory of Science and Technology on Multispectral Information Processing, School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China

    Chengjie Xu, Ying Zheng & Housheng Su

  3. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, China

    Michael Z. Q. Chen

  4. School of Electrical and Information Engineering, Hunan University of Technology, Zhuzhou, 412008, China

    Changfan Zhang

Authors
  1. Chengjie Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Housheng Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael Z. Q. Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Changfan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying Zheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xu, C., Zheng, Y., Su, H. et al. Cluster consensus for second-order mobile multi-agent systems via distributed adaptive pinning control under directed topology. Nonlinear Dyn 83, 1975–1985 (2016). https://doi.org/10.1007/s11071-015-2459-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2459-5

Keywords

Search

Navigation